Block and strictly chordal graphs.
Block graphs are graphs in which every biconnected component is a clique. They can also be characterized as chordal graphs that do not contain diamonds as induced subgraph [1]} (see Figure REF ).
A natural generalization of block graphs are strictly chordal graphs, also known as block
duplicate graphs, that are obtained from block graphs by adding true twins [2]}, [3]}, [4]}.
